Ridges, crests and sub-parabolic lines of evolving surfaces

International Journal of Computer Vision

Volumn 18, Issue 3, 1996, Pages 195-210

  Bruce, J W ^a   Giblin, P J ^a   Tari, F ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; MATHEMATICAL TECHNIQUES; MEDICAL IMAGING; PATTERN RECOGNITION;

CREST LINES; GENERIC SURFACE; RIDGE LINES; SUBPARABOLIC LINES;

COMPUTER VISION;

EID: 0030172963     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00123141     Document Type: Article

References (26)

1. Arnold, V.I. 1984; 1986; Third edition 1992. Catastrophe Theory. Springer-Verlag: New York-Heidelberg-Berlin.
2. Bruce, J.W. 1984. Generic reflections and projections. Math. Scand., 54:262-278.
3. Bruce, J.W. and Fidal, D.L. 1989. On binary differential equations and umbilics. Proc. Royal Soc. Edinburgh, Vol. 111A:147-168.
4. Bruce, J.W. and Wilkinson, T.C. 1991. Folding maps and focal sets. Proceedings of Warwick Symposium on Singularities, Springer Lecture Notes in Math., Vol. 1462:63-72, Springer-Verlag: Berlin-Heidelberg-New York.
5. Bruce, J.W. and Giblin, P.J., Second edition 1992. Curves and Singularities. Cambridge University Press: Cambridge, U.K.
6. Bruce, J.W. and Tari, F. 1994. Extrema of principal curvature and symmetry. To appear in Proc. Royal Soc. Edinburgh.
7. Bruce, J.W., Giblin, P.J., and Tari, F. 1995. Families of surfaces: Height functions. Gauss maps and duals. In W.L. Marar (Ed.), Real and Complex Singularities, Pitman Research Notes in Mathematics, Vol. 333, pp. 148-178.
8. Bruce, J.W., Giblin, P.J., and Tari, F. 1994a. Families of surfaces: Height functions and projections to planes. University of Liverpool, Preprint.
9. Bruce, J.W., Giblin, P.J., and Tari, F. 1994b. Families of surfaces: Focal sets, ridges and umbilics. University of Liverpool, Preprint.
10. Bruce, J.W., Giblin, P.J., and Tari, F. 1996. Parabolic curves of evolving surfaces. Int. J. Computer Vision, 17:291-306.
11. Colchester, A.C.F. 1990. Network representation of 2D and 3D images. In 3D Imaging in Medicine. K.H. Höne, H. Fuchs, and S. Pizer (Eds.), Springer-Verlag: New York-Berlin-Heidelberg, pp. 45-62.
12. Crowley, J.L. and Parker, A.C. 1984. A representation of shape based on peaks and ridges in the difference of low-pass transform. IEEE Trans. PAMI, 6:156-170.
13. Eisenhart, L.P. 1909. Differential Geometry. Ginn and Company: London
14. Gordon, A.P. 1991. Face recognition from depth maps and surface curvature. In Proceedings of SPIE Conference on Geometric Methods in Computer Vision, San Diego, CA.
15. Guéziec, A. 1995. Surface representation with deformable splines: using decoupled variables, IEEE Comp. Sci. and Eng. Mag. 2:69-80.
16. Koenderink, J. 1990. Solid Shape. M.I.T.Press: Cambridge, Mass.
17. Morris, R.J. 1991. Symmetry of Curves and the Geometry of Surfaces: Two Explorations with the aid of Computer Graphics. Ph.D. Thesis, University of Liverpool.
18. Morris, R.J. 1994. The sub-parabolic lines of a surface. To appear in The Mathematics of Surfaces VI (Brunel University, 1994), Clarendon Press: Oxford.
19. O'Neill, B. 1966. Elementary Differential Geometry. Academic Press: New York.
20. 3. Proceedings of Symposia in Pure Mathematics, Vol. 40, Part 2, pp. 379-394, Providence, R.I.: American Mathematical Society.
21. Porteous, I.R. 1994. Geometric Differentiation. Cambridge University Press: Cambridge, U.K..
22. Sander, P.T. and Zucker, S.W. 1992. Singularities of principal direction fields from 3-D images. IEEE Trans. PAMI, 14:309-317.
23. Sottomayer, J. and Guttierrez, C. 1982. Structurally stable configurations of lines of principal curvature. Astérisque, Vol. 98-99, pp. 195-215.
24. Thirion, J.-P. 1996. New feature points based on geometric invariants for 3D image registration. INRIA Research Report No. 1901; to appear in Int. J. Computer Vision.
25. Thirion, J.-P. and Gourdon, A. 1995. Computing the differential characteristics of isointensity surfaces, Computer Vision and Image Understanding, 61:190-202.
26. Wilkinson, T.C. 1991. The Geometry of Folding Maps, Ph.D. Thesis, University of Newcastle-upon-Tyne.